Steady meridional flow makes no first-order perturbation to the frequencies of helioseismic normal modes. It does, however, Doppler shift the local wavenumber, thereby distorting the eigenfunctions. For high-degree modes, whose peaks in a power spectrum are blended into continuous ridges, the effect of the distortion is to shift the locations of those ridges. From this blended superposition of modes, one can isolate oppositely directed wave components with the same local horizontal wavenumber and measure a frequency difference which can be safely used to infer the subsurface background flow. But such a procedure fails for the components of the more-deeply-penetrating low-degree modes that are not blended into ridges. Instead, one must analyze the spatial distortions explicitly. With a simple toy model, we illustrate one method by which that might be accomplished by measuring the spatial variation of the oscillation phase. We estimate that by this procedure it might be possible to infer meridional flow deep in the solar convection zone.
Using a 3D global solver of the linearized Euler equations, we model acoustic oscillations over background velocity flow fields of single-cell meridional circulation with deep and shallow return flows as well as double-cell meridional circulation with strong and weak reversals. The velocities are generated using a mean-field hydrodynamic and dynamo model -- moving through the regimes with minimal parameter changes; counter-rotation near the base of the tachocline is induced by sign inversion of the non-diffusive action of turbulent Reynolds stresses ($Λ$-effect) due to the radial inhomogeneity…
Accurate inference of solar meridional flow is of crucial importance for the understanding of solar dynamo process. Wave travel times, as measured on the surface, will change if the waves encounter perturbations e.g. in the sound speed or flows, as they propagate through the solar interior. Using functions called sensitivity kernels, we may image the underlying anomalies that cause measured shifts in travel times. The inference of large-scale structures e.g meridional circulation requires computing sensitivity kernels in spherical geometry. Mandal et al. (2017) have computed such spherical ker…
Global hydrodynamic simulations of internal solar dynamics have focused on replicating the conditions for solar-like differential rotation and meridional circulation using the results of helioseismic inversions as a constraint. Inferences of meridional circulation, however, have provided controversial results showing the possibility of one, two, or multiple cells along the radius. To resolve this controversy and develop a more robust understanding of global flow regimes in the solar interior, we apply a "forward-modeling" approach to the analysis of helioseismic signatures of meridional circul…
A key component of solar interior dynamics is the meridional circulation (MC), whose poleward component in the surface layers has been well observed. Time-distance helioseismic studies of the deep structure of MC, however, have yielded conflicting inferences. Here, following a summary of existing results we show how a large center-to-limb systematics (CLS) in the measured travel times of acoustic waves affect the inferences through an analysis of frequency dependence of CLS, using data from the Helioseismic and Doppler Imager (HMI) onboard Solar Dynamics Observatory (SDO). Our results point to…
We apply the helioseismic methodology of Legendre Function Decomposition to 88 months of Dopplergrams obtained by the Helioseismic and Magnetic Imager (HMI) as the basis of inferring the depth variation of the mean meridional flow, as averaged between 20 and 60 degrees latitude and in time, in both the northern and southern hemispheres. We develop and apply control procedures designed to assess and remove center-to-limb artifacts, using measurements obtained by performing the analysis with respect to artificial poles at the east and west limbs. Forward modeling is carried out, using sensitivit…
The south-north travel-time differences are measured by applying time-distance helioseismology to the MDI and HMI medium-degree Dopplergrams covering May 1996-April 2017. Our data analysis corrects for several sources of systematic effects: P-angle error, surface magnetic field effects, and center-to-limb variations. An interpretation of the travel-time measurements is obtained using a forward-modeling approach in the ray approximation. The travel-time differences are similar in the southern hemisphere for cycles 23 and 24. However, they differ in the northern hemisphere between cycles 23 and …
Today's picture of the internal solar rotation rate profile results essentially from helioseismic analyses of frequency splittings of resonant acoustic waves. Here we present another, complementary estimation of the internal solar rotation rate using the perturbation of the shape of the acoustic waves. For this purpose, we extend a global helioseismic approach developed previously for the investigation of the meridional flow \cite{schad11, schad12, schad13} to work on the components of the differential rotation. We discuss the effect of rotation on mode eigenfunctions and thereon based observa…
We present a 3-dimensional (3D) numerical solver of the linearized compressible Euler equations (GALE -- Global Acoustic Linearized Euler), used to model acoustic oscillations throughout the solar interior. The governing equations are solved in conservation form on a fully global spherical mesh ($0 \le ϕ\le 2π$, $0 \le θ\le π$, $0 \le r \le R_{\odot}$) over a background state generated by the standard Solar Model S. We implement an efficient pseudo-spectral computational method to calculate the contribution of the compressible material derivative dyad to internal velocity perturbations, comput…
Helioseismic inferences of large-scale flows in the solar interior necessitate accounting for the curvature of the Sun, both in interpreting systematic trends introduced in measurements as well as the sensitivity kernel that relates photospheric measurements to subsurface flow velocities. Additionally the inverse problem that relates measurements to model parameters needs to be well-posed to obtain accurate inferences, which necessitates a sparse set of parameters. Further, the sensitivity functions need to be computationally easy to evaluate. In this work we address these issues by demonstrat…
Context. In local helioseismology, the travel times of acoustic waves propagating in opposite directions along the same meridian inform us about horizontal flows in the north-south direction. The longitudinal averages of the north-south helioseismic travel-time shifts vary with the sunspot cycle. Aims. We aim to study the contribution of inflows into solar active regions to this solar-cycle variation. Methods. To do so, we identify the local flows around active regions in the horizontal flow maps obtained from correlation tracking of granulation in SDO/HMI continuum images. We compute the forw…
Oscillatory Phase and Acoustic Travel-Time Inconsistencies Measured between SDO/HMI and GONG Dopplergrams
Stanford University（斯坦福大学）；Indian Institute of Astrophysics（印度天体物理研究所）；National Solar Observatory（国家太阳观测台）；National Research University TIIAME（塔什干国立研究技术大学）
The results of determinations of the azimuthal and meridional velocities by time-distance helioseismology from Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from May 2010 to September 2020 at latitudes from -60° to +60° and depths to about 19 Mm below the photosphere are used to analyze spatiotemporal variations of the solar differential rotation and meridional circulation. The pattern of torsional oscillations, or latitudinal belts of alternating `fast' and `slow' zonal flows migrating from high latitudes towards the equator, is found to extend in the time--l…
Time--Distance Helioseismology Data Analysis Pipeline for Helioseismic and Magnetic Imager onboard Solar Dynamics Observatory (SDO/HMI) and Its Initial Results
Helioseismic waves observable at the solar surface can be used to probe the properties of the Sun's interior. By measuring helioseismic travel times between different location on the surface, flows and other interior properties can be inferred using so-called sensitivity kernels which relate the amount of travel-time shift with variations in interior proporties. In particular, sensitivity kernels for flows have been developed in the past, using either ray or Born approximation, and have been used to infer solar interior flows such as the meridional circulation which is of particular interest f…
Ensemble Kalman filter data assimilation in a Babcock-Leighton solar dynamo model: an observation system simulation experiment for reconstructing meridional flow-speed
We analyze spectral properties of solar convection in the range of depths from 0 to 19~Mm using subsurface flow maps obtained by the time-distance heiioseismology analysis of solar-oscillation data from the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from May 2010 to September 2020. The results reveal a rapid increase of the horizontal flow scales with the depth, from supergranulation to giant-cell scales, and support the evidence of large-scale convection, previously detected by tracking the motion of supergranular cells on the surface. The total power of c…
We build a hydrodynamical model for computing and understanding the Sun's large-scale high latitude flows, including Coriolis forces, turbulent diffusion of momentum and gyroscopic pumping. Side boundaries of the spherical 'polar cap', our computational domain, are located at latitudes $\geq 60^{\circ}$. Implementing observed low latitude flows as side boundary conditions, we solve the flow equations for a cartesian analog of the polar cap. The key parameter that determines whether there are nodes in the high latitude meridional flow is $ε=2 Ωn πH^2/ν$, in which $Ω$ is the interior rotation ra…
